The present invention relates to a method and apparatus for determining the amount of a gas adsorbed or desorbed by a solid in a manner such that the corresponding adsorption and/or desorption isotherm can be constructed from which in turn various morphological characteristics of the solid such as surface area, pore size distribution, and average pore volume, can be determined.
The measurement of morphological characteristics of solids, such as catalysts, catalyst supports, pigments, clays, minerals, and composite materials, has long been an outstanding goal of analytical chemistry.
For example, a very useful morphological characteristic of a solid is its surface area. One of the most widely used techniques for surface area determination is that of gas sorption. Gas sorption techniques utilize a theoretical model wherein the surface of the solid (i.e. the adsorbent) being characterized is viewed as being covered by a monolayer of closely packed molecules of an adsorbed gas (i.e. the adsorbate). If one can determine the amount (usually expressed in ml) of adsorbate in the monolayer, the area covered by the monolayer can then easily be calculated e.g. from the product of the number of molecules in the monolayer times the cross sectional area of each molecule. In 1938 Branauer, Emmett, and Teller described (J. Am. Chem. Soc. Vol. 60, 2309) a mathematical equation, referred to as the BET equation, for determining the amount of adsorbate in the monolayer from the absorption isotherm of the adsorbate. The absorption isotherm is a plot of the amount of the adsorbate adsorbed on a solid against either the relative pressure or the equilibrium pressure of the adsorbate at a constant temperature. In order to utilize the BET equation accurately to determine surface area, one must at least obtain a sufficient number of data points on the adsorption isotherm to be able to determine the point on the adsorption isotherm at which the "monolayer capacity" occurs. The "monolayer capacity" is a variable in the BET equation and represents the point on the adsorption isotherm wherein a monolayer of closely packed adsorbed molecules is present at the surface of the adsorbent. Since the monolayer capacity generally occurs at an adsorbate partial pressure of between about 0.8 and 2.5, one desires to known the adsorption isotherm at least over this range of partial pressures to be able to calculate the surface area from the BET equation. It is significant, however, that while the entire adsorption isotherm ranging from an adsorbate partial pressure of 0 to 1 (the adsorbate partial pressure is one way of expressing the equilibrium pressure of the adsorbate as a fraction of the pressure at which condensation of the adsorbate occurs under any set of constant volume and temperature conditions) need not be known for purposes of determining surface area alone, the information embodied in the entire adsorption isotherm is nonetheless very useful for other reasons as described hereinafter.
Thus, there is a strong incentive to develop analytical method which possess the capability of determining the entire adsorption isotherm.
Adsorption isotherms are conventionally determined by two general methods, namely, the gravimetric method, and the volumetric methods.
In the gravimetric method the amount of adsorbed gas at the equilibrium pressure is weighed with the aid of a microbalance. However, gravimetric methods possess the disadvantages of limitations in the choice of adsorbate (e.g. controlling a sample at liquid nitrogen temperatures is not feasible); effective temperature control of the sample is difficult to achieve; and sophisticated and expensive equipment is required to attain the high degree of sensitivity needed for the measurements. Volumetric devices, in contrast, are simpler and intrinsically more reliable.
In the volumetric method, the volume of the gas adsorbed in measured rather than the weight. Volumetric devices conventionally use nitrogen as the adsorbate at a temperature of -195.degree. C. These devices typically consist of a gas storage unit and a vacuum source unit connected in parallel to a volumetric measuring device, referred to as the doser unit, of known volume V.sub.1 ; such as a burette or pipette. The doser unit can alternately be connected to either the vacuum unit or the gas storage unit by a series of stopcocks. The doser unit in turn is connected in series through another stopcock to a sample unit, i.e. a chamber of known volume V.sub.2 which holds the solid to be tested. By manipulating the various stopcocks, the doser and sample units are evacuated, and the evacuated doser sealed off from the evacuated sample chamber. Nitrogen is permitted to slowly enter and fill the doser unit from the gas storage unit at which time the stopcocks are again manipulated to completely seal off the doser while the nitrogen pressure therein is measured. When a constant pressure, P.sub.1, in the doser is achieved, the stopcock separating the sample chamber and doser is opened allowing the N.sub.2 in the doser to expand into the sample chamber, the sample chamber and doser together defining a third Volume V.sub.3 (i.e. V.sub. 1 +V.sub.2). When the pressure in V.sub.3 is constant, indicative of adsorption equilibrium, it is measured. This equilibrium pressure is used to calculate the total number of moles of N.sub.2 that remains in the gas phase. The number of moles of N.sub.2 adsorbed on the solid is equal to the moles of N.sub.2 initially present in Volume V.sub.1 of the doser plus the moles of N.sub.2 in the sample chamber defining Volume V.sub.2 (the moles in Volume V.sub.2 for the initial run is 0 but increases with each successive run), less the moles of gaseous N.sub.2 in Volume V.sub.3, after equilibration. The combined data of the amount of N.sub.2 adsorbed at a particular equilibrium pressure constitutes a single point on the adsorption isotherm. The above procedure is repeated each time to obtain additional points on the adsorption isotherm. Each successive run increases the pressure in the sample chamber until at atmospheric pressure, saturation of the sample solid which condensed N.sub.2 occurs, i.e., condensation of N.sub.2 takes place on the sample and the free space in the sample holder. Conventional practice is to generate about 8 data points on the absorption isotherm for surface area determinations. It generally takes one hour per data point to obtain pressure equilibration. Needless to say, this method is very time consuming, requiring 2 delays per data point waiting for equilibration, and the adsorption isotherm data points are generated on a discontinuous basis. A detailed summary of this method is provided in the review paper "The BET Method of Analysis of Gas Adsorption Data and Its Relevance To The Calculation of Surface Areas" by Dollimore, D., Sponner, P., and Turner, A., Surface Technology, Vol. 4, p. 121-160 (1976).
Discontinuous volumetric gas sorption units have been improved by automating the opening and closing of the stopcocks and by increasing the number of sample chambers and doser units. The time for equilibration has been shortened by experimentally determining equilibration times and programming the automated system to respond to a preset equilibration time. However, this does not alter the discontinuous nature of unit operations and still requires excessive waiting time to provide relatively few data points.
Bosch and Peppelenbos describe in the Journal of Physics E: Scientific Instruments, Vol. 10, p. 605-608 (1977) a dynamic method for determining data points on the adsorption isotherm. In accordance with this method a gaseous adsorbate is introduced into an evacuated sample chamber of known volume and temperature (e.g. liquid nitrogen temperature) at what is alleged to be a constant volume flow rate (e.g., about 1 cm.sup.3 STP min.sup.-1 at a partial pressure of about 0.25) while measuring the pressure. The alleged constant volume flow rate is achieved by introducing the adsorbate into the sample chamber through a capillary tube. The amount of adsorbate adsorbed by the adsorbent is calculated by comparing the pressure increase in the sample chamber in the presence of an adsorbing sample against time, with the pressure increase in a blank (i.e. a sample chamber having no adsorbing sample present therein) against time. In the presence of an adsorbent, the adsorbate gas will be partly adsorbed and it takes more time to reach a certain pressure than it does when using the blank. Thus, the volume of gas adsorbed by the sample (Va) at a particular pressure is calculated from the equation: EQU [Va=.phi.V(STP).DELTA.t].sub.p
wherein .phi.V (STP) is the volume flow through the capillary tube (cm.sup.3 min..sup.-1) at standard temperature and pressure, and .DELTA.t is the extra time in minutes to reach pressure P compared to a blank experiment. While the volume flow rate is treated as being constant for purposes of a single data point on the adsorption isotherm, it is in fact acknowledged at page 608 that the flow rate is not constant, e.g. when nitrogen is employed as the adsorbate, thereby requiring much more laborious calculations to generate even a partial adsorption isotherm. Other disadvantages of this method stem from the use of a capillary tube to regulate flow. For example, the characteristics of a fixed capillary tube change with time and environmental conditions. Thus, fluctuations in ambient conditions induce fluctuations in the adsorbate flow rate as a result of thermoexpansion or contraction of the capillary tube. Fixed capillaries are not only difficult to manufacture within specified ranges but they are subject to plugging with solid adsorbent upon desorption and are so fragile that they need frequent replacement. A fixed leak capillary cannot be adjusted to control the flow of gas and provide optimum conditions dictated by the type of adsorbent sample being employed. More importantly, however, is the inaccuracy (e.g. 10-15% and higher) introduced into the adsorbtion isotherm and surface area determination of very high surface area materials, e.g. greater than 500 m.sup.2 /g if it is assumed that the volume flow rate is constant. This stems from the fact that the higher the surface area of the sample the longer it will take to achieve equilibrium pressure. Consequently, for a given weight of sample, the higher the surface area, the lower the flow rate must be, and the lower the flow rate the smaller the I.D. of the capillary tube must be, thereby enhancing the sensitivity of the flow rate to environmental fluctuations. Apart from the environmentally induced fluctuations in flow rate as described above, adsorbate backpressure, which builds up in the sample holder as one approaches higher partial pressures in the adsorbtion isotherm, also changes, i.e. reduces, the flow rate. It is admitted in Bosch et al pg. 606 that backpressure even at a partial pressure of about 0.2 results in a 0.6% decrease in the flow rate. Such backpressure induced volume flow fluctuations are magnified as one continues the collection of data points at higher points on the adsorbtion isotherm. Consequently, one is forced to accept increasingly larger experimental errors over the course of the experiment, or where possible mathematically compensate for such fluctuations by extremely complicated integration procedures with respect to the blank and the sample run.
In addition, there are intrinsic limitations in use of a capillary, stemming from the need to maintain the flow rate of the adsorbate to be not greater than the equilibration rate of adsorption, which prevent attaining a complete adsorption isotherm from a practical standpoint. For example, in a capillary system the flow rate is proportional to the pressure drop across the capillary. Consequently, since the initial flow rate is very low, backpressure reduces the flow rate even further so that after reaching about 70 to 80% of the adsorption isotherm, the flow rate becomes almost non-existent.
Innes, U.S. Pat. No. 2,729,969 discloses a capillary method very similar to Bosch et al. The system described therein has the same disadvantages discussed above attributable to the use of a capillary to regulate the flow of the adsorbate. Adsorbate introduction is conducted at a partial pressure regime of about 0.1 to 0.3 at a flow rate at about 7 to about 10 cc/min. It is acknowledged at col. 6, lines 45 et seq, that equilibrium pressure conditions did not exist at a flow rate of either 10 cc/min or 7 cc/min when employing small pore (hence high surface area) samples, i.e. the flow rate was greater than the adsorbate equilibration rate of adsorption. However, to obtain lower rates, either smaller diameter capillary tubes must be employed thereby increasing the sensitivity of the flow rate to environmental induced flow rate fluctuations or a lower fore pressure must be employed thereby increasing the sensitivity of the flow rate to backpressure induced flow rate fluctuations. At col. 4, lines 5 et seq it is stated that the flow rate is constant as shown at FIG. 4 therein. However, FIG. 4 of this patent illustrates a flow time of only 150 seconds using only 11 data points. Bosch et al also attempt to support allegations of constant flow rate with a similar plot using a flow time of 60 minutes and 6 data points. None of this data illustrate a constant flow rate over flow times of about 4 hrs. which are typically needed if the flow rate is to be maintained below the equilibration rate of adsorption of most samples of initially unknown surface areas for a time sufficient to achieve a partial pressure in the monolayer capacity range, e.g. 0.8-2.5. As stated above, environmental induced flow rate fluctuations accumulate over extended periods of time. Consequently, the data used to support allegations of constant flow rate for the capillary method do not reflect operating conditions that a commercially successful apparatus would be required to perform under.
Another significant disadvantage of the fixed leak capillary method develops if one attempts to employ the Bosch et al capillary system for determining desorption isotherms (the use of which is discussed hereinafter). In a desorption experiment, a preadsorbed gas would be removed from the surface of the sample through the capillary which is connected to a vacuum source. In this procedure the pressure in the sample holder decreases with time. Consequently, the pressure differential between both ends of the capillary is reduced over the course of the desorption experiment. Since this pressure differential is the driving force which removes the preadsorbed gas from the sample chamber, even a partial desorption experiment will take between about 20 and about 40 hours to complete. Accordingly, not only is the capillary desorption method time consuming, but the environmentally induced volume flow rate fluctuations accumulate over such extended periods, again necessitating complicated mathematical corrections to determine the actual volume flow rate (and therefore the actual amount of gas desorbed at any given equilibrium pressure) at any given time during the procedure. Such errors are not discussed in Bosch et al, since they are not concerned with desorption.
Innes does disclose the use of the capillary system for desorption. However, apparently because of the problems associated with evacuating a chamber through a capillary tube discussed above, he is forced to heat the nitrogen adsorbed on the sample at room temperature rather than desorb at liquid nitrogen temperatures. Taking the sample holder in and out of liquid nitrogen not only complicates the procedure, but it introduces significant error in the determination of the volume of the system which is under equilibrium conditions at, for example, liquid nitrogen temperatures. Such discontinuity causes the actual temperature of the sample to deviate from the liquid nitrogen temperature. A 1.degree. C. variance in the actual sample temperature relative to the liquid nitrogen temperature will invalidate the test results.
In summary, neither of the capillary methods disclosed by Bosch et al and Innes disclose flow rates below 1 ml/min at STP, which are substantially constant as defined herein for any period of time.
Desorption isotherms are important because various mathematical equations are known which enable one to calculate the pore size distribution of a solid sample from the data embodied therein. A desorption isotherm is a plot of the amount of a preadsorbed gaseous material (referred herein as the desorbate) desorbed from a solid against the equilibrium pressure of the desorbate at a constant temperature. The desorption isotherm differs from the adsorption isotherm in that it is constructed starting with a solid saturated with the desorbate and gradually reducing the pressure over the solid to near absolute vacuum. In constrast, the adsorption isotherm starts with an evacuated solid sample and increases the pressure of a gaseous adsorbate in contact therewith until sample saturation is reached. The adsorption and desorption isotherms are collectively known as the sorption isotherm. Gas-solid interaction can cause at least a portion of the desorption path of the sorption isotherm to lie higher on the isotherm plot than the adsorption path. The failure of the desorption path to duplicate the adsorption path of the isotherm is commonly referred to as hysteresis. The two most common forms of hysteresis are referred to as closed loop and open loop. In the closed loop hysteresis behavior, the desorption path of the isotherm eventually rejoins the adsorption path at some low relative pressure. Closed loop hysteresis is normally associated with porosity in the sample being tested. For example, at the start of the desorption isotherm, the pores of the sample are saturated and filled with the desorbate. As desorption occurs, capillary action delays desorption of the desorbate present within the pores, such that a lower pressure is required to evacuate the pores relative to the pressure which initiated the filling of the pores during adsorption. This delay is expressed as closed loop hysteresis behavior of the sorption isotherm. Open loop hysteresis is characterized by the failure of the desorption path of the isotherm to rejoin with the adsorption path. Open loop hysteresis is usually associated with some measurable amount of irreversible adsorption, which typically occurs when the gas reacts with the solid sample upon adsorption, conventionally referred to as chemisorption. Consequently on desorption, less material will desorb than was initially adsorbed, giving rise to an open loop in the sorption isotherm.
By intentionally inducing chemisorption much can be learned about the surface of the solid sample. For example, chemisorption can be employed to determine the % dispersion and surface area of microscopic particles of a catalyst deposited on a support by employing a gaseous adsorbate which will undergo chemisorption with the catalyst particles but not the support.
Other information in the substantially complete sorption isotherm permits the determination of total pore volume, average pore size, and pore shape (e.g., slits vs. circular pores).
The above discussion highlights only a few of the incentives for obtaining substantially complete pictures of the entire sorption isotherm rather than narrow segments thereof, and any method or device capable of producing substantially complete sorption isotherms quickly and accurately possesses substantial advantages over capillary methods of the Bosch et al or Innes.
An alternative method for determining adsorption isotherms has been reported in an article by Nelsen, & Eggersten, Analytical Chem., Vol. 30 p. 13-87 (1958) titled "Adsorption Measurements By A Continuous Flow Method". In this method, nitrogen is adsorbed by the adsorbent at liquid nitrogen temperature from a gas stream of nitrogen and helium, and eluted upon warming the sample. The nitrogen liberated is measured by thermal conductivity. Thus, the amount of adsorbed gas is determined by concentration measurements in a continuous flow system at atmospheric pressure rather than by pressure volume measurements at below atmospheric pressure. This method is referred to herein as a chromatographic method for determining adsorption isotherms because of its resemblance to chromatography techniques. Two requirements of this method are steady flow of carrier and adsorbate gases, and through mixing of the two gases, insitu. In the Nelsen et al method, flow control is provided by capillary tubes. However in an article by Farey, and Tucker, Analytical Chem., Vol. 43, No. 10 p. 1307 (1971) titled "Determination of Surface Areas By An Improved Continuous Flow Method", the capillary tubes are replaced with a series of pressure and mass flow controllers in an attempt to achieve steady flow (see also, Bhat, R., and Krishnamoorthy, T., Indian Journal of Technology, Vol. 14, p. 170 (1976)). Nitrogen flow rates suitable for the experiment ranged from 2 to 20 ml/min. However, it is acknowledged at p. 1309 that flow rates through the detector would momentarily change during rapid temperature changes encountered in the adsorption/desorption cycle. This is not a problem in the Farey et al chromatographic method since each data point is generated on a discontinuous basis over a relatively short period of time (e.g. 20 min.) and it is within the capabilities of the mass flow controller to compensate for these fluctuations during the production of discontinous peaks, i.e. data points. The short duration needed for each peak also avoids the accumulation of error generated by environmental fluctuations over extended periods of time. In contrast, the method of the present invention cannot tolerate even minor uncontrolled fluctuations in the mass flow rate during the course of the analysis (e.g. about 4 hrs. for adsorption and 12 hrs. for desorption) except as defined hereinafter. The attainment of this goal in the present invention is even further complicated by the fact that mass flow rates in the range of 0.2 to 0.4 ml/min are typically employed. Such low flow rates are preferred to avoid administering or desorbing the gas to the adsorbent or desorbent respectively at a rate greater than the equilibration rate of adsorption or desorption, which typically is very low for high surface area materials. Low flow rates are particularly troublesome and cannot be achieved by conventional mass flow controllers at very low pressures where the thermal conductivity of the gases passing therethrough is very low. This stems from the fact that conventional mass flow controllers typically utilize the thermal conductivity of the gas passing therethrough as a way of metering the flow of the gas. This problem is exacerbated by environmental fluctuations in temperature which cause unwanted, uncontrolled, and accumulated fluctuations in the flow meter sensing elements of conventional mass flow controllers. Furthermore, the low thermal conductivity of gases at low pressure and low flow rates cause the environmentally induced fluctuations in the flow rate to impart a greater contribution to the total error in the flow rate relative to the use of conventional flow rates and pressures. Conventional mass flow controllers therefore are unsuitable for use in practicing the method of the present invention. Conventional flow meters and thermal valves which make up the primary components of a conventional mass flow controller are described in U.S. Pat. Nos. 3,650,505; 3,851,526; 3,938,384; and 4,056,975.
In view of the above, it is evident that there has been a continuing search for quicker, simpler, and more accurate methods and apparatus for determining sorption isotherms. The present invention was developed in response to this search.